Weight-monodromy conjecture over equal characteristic local fields

Details Weight-monodromy conjecture over equal characteristic local fields Weight-monodromy conjecture over equal characteristic local fields

2003-08-14

arxiv.org/abs/math/0308141v2

Mathematics

Number Theory

12 pages, AMS LaTeX, revised version, to appear in the American Journal of Mathematics

Scientific paper

The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the monodromy filtration defined on the $l$-adic \'etale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fields. We also prove that the weight spectral sequences degenerate at $E_2$ in any characteristic without using log geometry. Moreover, as an application, we give a modulo $p>0$ reduction proof of a Hodge analogue previously considered by Steenbrink.

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